Chop the cooked chicken into small, bite-sized cubes and place in a large mixing bowl.
Chop the celery and add it to the bowl with the chicken.
In a separate bowl, whip the heavy whipping cream until slightly thickened, then whisk in the lemon juice, mayonnaise, salt, and pepper until smooth.
Add the chopped parsley, sliced almonds, and halved grapes to the chicken and celery.
Pour the dressing over the chicken mixture and gently toss until everything is evenly coated.
Cover and refrigerate for at least 1 hour before serving to allow flavors to meld.